f(x) =
{−8 if −3 ≤ x ≤ 0
{x if 0 < x ≤ 3
Evaluate the given expressions.
a)f(-1)=
b)f(0)=
(^Teach how to do this.)
Duplicate the graphs. What is the formula?
a)(−8)*(x > −3)*(x >= 0) + (x)*(x <= 0)*(x > 3)
b)(−8)*(x >= −3)*(x <= 0) + (x)*(x > 0)*(x <= 3)
c) (−8)*(x <= 0) + (x)*(x <= 3)
d)(−8)*(x >= −3) + (x)*(x > 0)
Thank You.
To evaluate the given expressions, we need to substitute the values of x into the function f(x) and simplify the expression according to the given conditions.
a) To evaluate f(-1), we substitute x = -1 into the function f(x):
f(-1) = -8 (since -3 ≤ -1 ≤ 0)
b) To evaluate f(0), we substitute x = 0 into the function f(x):
f(0) = 0 (since 0 is not greater than 0 or less than or equal to 3)
Now, let's understand how to arrive at the provided formulas for the graph.
The given function, f(x), has two parts based on the range of x. For -3 ≤ x ≤ 0, the output is -8, and for 0 < x ≤ 3, the output is x itself.
To duplicate the graph using a formula, we need to use conditional statements and mathematical operators:
a) The formula for duplicating the graph of f(x) for the range -3 ≤ x ≤ 0 is:
(−8)*(x > -3)*(x ≥ 0) + (x)*(x ≤ 0)*(x > 3)
This formula checks if x is greater than -3 (x > -3) and also if x is greater than or equal to 0 (x ≥ 0). If both conditions are true, it evaluates to -8 times the result of multiplying the two conditions. If the conditions are not satisfied, it evaluates to 0.
Next, it checks if x is less than or equal to 0 (x ≤ 0) and also if x is greater than 3 (x > 3). If both conditions are true, it evaluates to x times the result of multiplying the two conditions. If the conditions are not satisfied, it evaluates to 0.
b) The formula for duplicating the graph of f(x) for the range 0 < x ≤ 3 is:
(−8)*(x ≥ -3)*(x ≤ 0) + (x)*(x > 0)*(x ≤ 3)
This formula follows a similar logic as in the previous formula. It checks if x is greater than or equal to -3 (x ≥ -3) and also if x is less than or equal to 0 (x ≤ 0). If both conditions are true, it evaluates to -8 times the result of multiplying the two conditions. If the conditions are not satisfied, it evaluates to 0.
Next, it checks if x is greater than 0 (x > 0) and also if x is less than or equal to 3 (x ≤ 3). If both conditions are true, it evaluates to x times the result of multiplying the two conditions. If the conditions are not satisfied, it evaluates to 0.
c) and d) The formula options c) and d) do not accurately represent the given function f(x) and its conditions. Hence, they are not valid formulas for duplicating the graph.
If you have any further questions, please let me know.